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cents

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Frequency ratio f2 / f1

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Frequency ratio f2 / f1

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cents

Fill out the gray boxes and click at the calculation bar.

How many cents are in a hertz?
There is no conversion from Hz to cents and vice versa. Scroll down to the bottom: "Table of Cent Difference".Statement: Cent is a logarithmic unit of measure of an interval, and that is a dimensionless "frequency ratio" of f2 / f1.

3.322038403 is a conversion factor that converts base 2 logarithms to base 10 logarithms.
1 Cent = 2(1/1200) = 1.0005777895065548592967925757932
One cent is thus the number that multiplied by itself 1200 times results in the number 2.
The cent is an interval which is calculated from the interval frequency ratio as follows:
(In of the interval frequency ratio / ln 2)×1200 = cents value of the interval.
An interval of a halftone is equivalent to: 2(1/12) = 1,0594630943592952645618252949463.
That is: [ln (2(1/12)) / ln (2)]×1200 cent = 100 cent.

Formulas: f = 440 × 2(−58/12) × (2(1/12))n and f = 440 × 2((n−58)/12)
The original source program of Iain W. Bird is still faulty:http://www.birdsoft.demon.co.uk/music/notecalc.htmThe frequency of 440 Hz is the concert pitch note A4.
If someone tells you different, this person is in error; see also:

Question: How can I convert cents to Hz?
Answer: You cannot convert cents to hertz, because cents are not a frequency.
cents are the measurement between intervals, that is a "frequency ratio" f2/f1.

Here's a Table of Cents Difference for some frequencies close around 440 Hz:

Frequency

Difference

435 Hz

−19.78 cents

436 Hz

−15.81 cents

437 Hz

−11.84 cents

438 Hz

−7.89 cents

439 Hz

−3.94 cents

440 Hz

±0 cent

441 Hz

+3.93 cents

442 Hz

+7.85 cents

443 Hz

+11.76 cents

444 Hz

+15.67 cents

445 Hz

+19.56 cents

So, the conversion factor 4 cents / Hz is valid for the purposes of tuning as an exception only very close around 440 Hz.There is no conversion from Hz to cents and vice versa.Statement: Cent is a logarithmic unit of measure of an interval, and that is a
dimensionless "frequency ratio" of f2 / f1.